حساسیت پارامتری تجزیه و تحلیل برای FEA فشرده سازی گرم فولاد

This paper reports a system for quantifying and comparing the sensitivity of a thermomechanical finite element analysis (FEA) of forging to variations in different input parameters. The results of applying the method to analyses of simple upsetting, impression-die forging and backward extrusion of hot steel are also described. The number of parameters in a thermomechanical FEA of forging make it impractical to investigate all of them, so the investigations were restricted to the parameters that define the flow stress of the forged steel and heat transfer and friction at the die–workpiece interface. Theoretical forging investigations of the kind described should be compared with the results of physical forging trials. This comparison would indicate whether or not more work characterising parameters for FEA of forging were justified.

Despite a scarcity of yield strength data for metals subjected to forging conditions finite element analysis (FEA) is a tool that can be used to improve the understanding of industrial forging. A large number of mechanical and thermal parameter values, which are used to characterise the process, are used in a thermomechanical FEA of forging. It is obvious that whereas the results of an FEA of forging will be significantly affected by variations in some of these parameter values, the effect of similar variations in other parameter values will be of little consequence. Investigations of the effect of parameter variations are important because they provide a guide to the level of uncertainty of the parameters, which is acceptable in relation to the results that they yield. The parameters that have the greater effect should be specified with greater accuracy than those whose effect is small. Many FE analyses of industrial forging have been reported. See, e.g. [1], [2], [3] and [4]. However, investigations of the effect that variations in input parameters have on the results of FEA of forging are not widely reported; only three such investigations were found in a recent literature survey. One of these, carried out by Majerus et al. [5] for an axisymmetric analysis of hot isothermal forging looked at the effect that changing the constant-shear friction factor at the die–workpiece interface from 0.085 to 0.225 had on an FE deformation grid. Ou and Balendra [6] examined the effect that changing the Coulomb friction coefficient had on a plain-strain isothermal FEA of forging an aerofoil blade. Increasing the Coulomb friction coefficient from 0.1 to 0.2 increased the computed forging load by between 35 and 45%. In a third investigation, Saigal et al. [7] examined the influence that the initial die temperature and ram velocity had on a coupled thermomechanical plane-strain FEA of hot forging. The analysis examined was of forging a compressor blade. The response of the analysis to die temperature was that if it was increased from 300 to 700 °F the forging load decreased by 9% and the average temperature of the workpiece increased by 43 °F. Increasing the initial ram velocity from 15 to 25 in./s decreased the forging load by 25.2% and increased the average temperature of the workpiece by 36 °F. In the first two of these investigations the analyses considered were isothermal, when in fact most hot forging does not take place under isothermal conditions, and no comparisons of the reported effects with the effect of variations in other parameters were made. In the third investigation the analysis was thermomechanical. However, the parameters investigated were the ram velocity and die temperatures, which are well-controlled and understood in industry. It is more useful to investigate the effects of the parameters that define the properties of the forged metal and the tool–workpiece interface since it is these that industry faces the greatest uncertainties over. This investigation is of the effects of these parameters on three thermomechanical finite element analyses of forging. The use of a full-factorial design of experiment in the investigation makes it possible to eliminate the interacting effects that varying the thermal and mechanical parameters had on the results.

Parametric sensitivity analyses have been performed for three finite element analyses of hot steel forging. The results provide a useful guide to which of the parameter changes investigated were important in each analysis. As well as helping to comprehend FEA of metal forging, the results also quantify key effects in three industrial forging operations in a way that is impossible using practical experiments. The meaning of the results is limited by the fact that they are peculiar to the unique incremental changes in value administered to the parameters. For a parametric sensitivity analysis, which addresses this limitation by investigating direct correlations between FEA, forging parameters and results see [14]. A step forward would be to compare the results of physical forging trials with those of theoretical forging trials. Variations in the results of an actual industrial forging process should be compared with variations in the results of single-step FEA experiments for the process. This investigation would indicate if more work characterising parameters for FEA of forging were justified. If a level of uncertainty in an input parameter caused variations in FEA results, which were smaller than the variation in results encountered in practice, this uncertainty would be acceptable. This outcome would indicate that further investigations of the parameter value were unnecessary. If the variations were greater than those encountered in practice, the uncertainty in the input parameter would be unacceptable. This outcome would justify the additional work needed to characterise the parameter with more precision. For instance, suppose the variation in load recorded in an industrial press for a particular forging process is ±5 t. If in an FEA of the process, increasing the friction factor characterising the die–workpiece interface from 0.1 to 0.2 caused the forging load to increase by 2 t it would not be necessary to determine friction factor with any more certainty. However, if this increase in friction factor caused the forging load to rise by 20 t this uncertainty in friction factor would be unacceptable and the result would indicate that the die–workpiece friction factor should be determined with more precision.